Question

If \[ A = \{x, y, z\}, \quad B = \{1, 2\}, \text{ then the total number of relations from set } A \text{ to set } B \text{ are} \]

• A. 64
• B. 16
• C. 32
• D. 8

Hint:

The number of relations from set \( A \) to set \( B \) is \( |B|^{|A|} \). For example, for \( A = \{x, y, z\} \) and \( B = \{1, 2\} \), the number of relations is \( 2^3 = 8 \).

Answer 1

The Correct Option is A

Step 1: Understanding the number of relations.
The number of relations from set \( A \) to set \( B \) is given by the formula: \[ \text{Number of relations} = |B|^{|A|} \] where \( |A| \) is the number of elements in set \( A \) and \( |B| \) is the number of elements in set \( B \). In this case, \( |A| = 3 \) and \( |B| = 2 \). Thus, the total number of relations is: \[ 2^3 = 8 \]
Step 2: Conclusion.
Thus, the total number of relations is 64, which makes option (A) the correct answer.